When Gordon Brown announced the government's plans to change the law on the allocation of social housing yesterday he must have known that he would reopen the debate on race and waiting lists, an issue the fascist British National party has long sought to exploit. Indeed it is something that has been used by rightwing politicians in local politics for many years, as anyone who has heard the arguments for "sons and daughters" housing will know.

The difficulties people encounter in getting a good affordable home are nothing to do with immigration. It is a myth that should not be indulged. There is a strand of argument that says the way to beat the BNP is to occupy some of its territory, steal their clothes. In fact every time mainstream political parties adopt this course the opposite happens – its territory is legitimised. If instead of trying to demolish their lies and distortions we give ground to the BNP, it will prosper. Pandering to the BNP or the lies that it has promoted and exploited does not weaken it. It strengthens its arguments and creates a vicious circle that allows the far right to come back for yet more concessions.

Brown's relaunch document, Building Britain's Future (pdf), says the government will "change the current rules for allocating council and other social housing, enabling local authorities to give more priority to local people and those who have spent a long time on a waiting list". This section of the government's programme sends a signal to those who have swallowed the argument that "local people" are being forced out of social rented housing by migrants, asylum seekers and others, that the government accepts there is a problem.

We have been through this at least once before, when Margaret Hodge set out a similar case two years ago. Yet as we saw in Barking and Dagenham, the far right's arguments about the recipients of social rented housing are a lie. The BNP campaigned in that borough on the claim that newcomers to the area, notably Africans, were being given preferential treatment on council waiting lists. The truth was different. The majority of Africans and other ethnic minority communities in Barking were living in private accommodation they paid for themselves. Most newly arrived migrants and asylum seekers are in fact barred from gaining access to social housing. The BNP continually seeks to racialise the housing debate, as Jon Cruddas has put it. The government should not permit it to succeed by conceding a false case.

We now face the prospect of an endless series of arguments over what the government's proposal means in practice, which will only give more space for racist myths to be bandied around. It will also raise real practical issues. At what point, for example, will the length of time someone has been waiting for a home give them preference over someone in greater housing need?

It is indeed the case that hundreds of thousands of people in Britain – black, Asian and white alike – are disadvantaged because of the absence of decent affordable housing. But this was not caused by migration. It is because first the Tory governments of Margaret Thatcher and John Major decimated the supply of new cheap homes; and then Labour squandered the opportunity of the 1997 election victory to press ahead with new house building. Labour failed to release the resources local authorities needed to build new homes and ignored households that desperately needed new cheap homes for rent. In the latter years of the Labour government there has been a recognition that too few homes are being built and greater resources are being committed to building cheap rented homes. But it will take many more homes and much more progress to roll back the deep disaffection and anger that exists over the failure to solve people's housing needs.

None of these circumstances are the fault of Britain's ethnic minority populations, whether longstanding or recent arrivals – it is the fault of politicians.

It seems the government has learned little from the debacle over its disastrous slogan "British jobs for British workers". Labour needs to start learning the lesson that defeating fascism cannot be done by first conceding to it.